Petit ensemble

Schweitz was the first to recognize that the definition of pressure is a problem in the physics of an open system. He argued that the classical result based on the properties of a closed, isolated system - a petit ensemble - must be recast in terms of an open system, a system with permeable walls, replacing the petit ensemble with the grand ensemble. This he did for both a classical... 

Schweitz proceeded to show that for a gas with an isotropic and uniform distribution of momentum, Zs reduces to —3pv, and in the absence of internal forces, one obtains 2T = 3pv, a statement of the ideal gas equation. One notes that the derivation is based on the exchange of momentum through imaginary walls, while in the case of a petit ensemble, the derivation is based on the action of forces exerted on the particles by impenetrable walls. Schweitz concludes with a discussion of the use by Slater [14], March [20] and Ross [21] of the virial theorem for a petit ensemble stated in the form... 

Soient M le sous-ensemble de ens(G) reunion des ensembles sous-jacents aux sous-groupes M(n) pour tout n, H le sous-schema ferme rdduit de G ayant l adh rence de M pour espace sous-jacent. Comme M(n) est etale sur k done rAduit, M(n) est corite-nu dans H et par suite, H est le plus petit sous-schdma ferme de G qui majore M(n) pour tout n. Soit maintenant k une extension algSbriquement close de k. Par construction, les sous-schAmas... 

A third form of the fundamental equation will be useful when we come to discuss the statistical mechanics in Chapter 4. The free energy F is the proper thermodynamic function to associate with the (petit) canonical ensemUe, but it is often more convenient to work with die grand canonical ensemble, for whidi the appropriate potential is O, where... 

---